Abstract: The discovery that AGN at the centers of galaxy clusters can deposit upward of 10^61 \rm erg in a single outburst has changed our understanding of the thermodynamic history of the hot gas in clusters. The radio jets emerging from the cD galaxy in the MS0735.6+7421 cluster have deposited ~ 6 \times 10^61 erg into the X-ray-emitting gas. This is enough energy to create an enormous system of cavities and shock fronts, to drive a massive outflow from the AGN, and to quench a cooling flow. \it Chandra X-ray images of this and other systems show that the radio jets compress and heat the gas, and there is growing evidence that cool, low-entropy gas is being uplifted from the center and being redistributed throughout the cluster. In some clusters, star formation and cool (10^4 K) gas are found along the edges of the radio lobes and cavities. We propose to obtain deep H(alpha) and \textitU-, \textitR-, and \textitI-band images of this cluster to examine the relationships between cool gas, star formation, and the cavity and shock systems. The proposed observations will provide constraints on the feedback process that appears to be operating in cooling flow clusters, and will provide a map of the nebular emission and young stars for future spectroscopic investigations. This thesis proposal was granted time in 2005A; however, no data were collected due to poor weather.